High School

Select the correct answer.

Create and solve a linear equation that represents the model, where circles and a square are shown evenly balanced on a balance beam.

A. [tex]x + 7 = 12 ; x = 5[/tex]

B. [tex]x = 5 + 7 ; x = 12[/tex]

C. [tex]x + 5 = 7 ; x = 2[/tex]

D. [tex]x + 7 = 5 ; x = -2[/tex]

Answer :

To solve the problem, we need to analyze each linear equation option given and find out which one is balanced correctly:

1. Equation: [tex]\( x + 7 = 12 \)[/tex]
- Solution: To solve for [tex]\( x \)[/tex], you subtract 7 from both sides:
[tex]\[
x = 12 - 7
\][/tex]
[tex]\[
x = 5
\][/tex]
This means that when [tex]\( x + 7 \)[/tex] equals 12, the value of [tex]\( x \)[/tex] is 5.

2. Equation: [tex]\( x = 5 + 7 \)[/tex]
- Solution: Here, [tex]\( x \)[/tex] is directly given as the sum:
[tex]\[
x = 5 + 7
\][/tex]
[tex]\[
x = 12
\][/tex]
This means [tex]\( x \)[/tex] is 12.

3. Equation: [tex]\( x + 5 = 7 \)[/tex]
- Solution: To solve for [tex]\( x \)[/tex], subtract 5 from both sides:
[tex]\[
x = 7 - 5
\][/tex]
[tex]\[
x = 2
\][/tex]
This means that when [tex]\( x + 5 \)[/tex] equals 7, the value of [tex]\( x \)[/tex] is 2.

4. Equation: [tex]\( x + 7 = 5 \)[/tex]
- Solution: To solve for [tex]\( x \)[/tex], subtract 7 from both sides:
[tex]\[
x = 5 - 7
\][/tex]
[tex]\[
x = -2
\][/tex]
This means that when [tex]\( x + 7 \)[/tex] equals 5, the value of [tex]\( x \)[/tex] is -2.

After solving all these equations, the matching solutions for the equations are:
- [tex]\( x + 7 = 12 \)[/tex] with [tex]\( x = 5 \)[/tex]
- [tex]\( x = 5 + 7 \)[/tex] with [tex]\( x = 12 \)[/tex]
- [tex]\( x + 5 = 7 \)[/tex] with [tex]\( x = 2 \)[/tex]
- [tex]\( x + 7 = 5 \)[/tex] with [tex]\( x = -2 \)[/tex]

The correct answer to the original question is [tex]\( x + 7 = 12 ; x = 5 \)[/tex], which balances the model as described.

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